1. Field of the Invention
This invention relates to the field of seismic imaging, particularly to two-dimensional and three-dimensional migration of surface seismic data. It consists of a method for efficiently obtaining an accurate velocity model, which model can be used in migration of seismic data.
2. Related Art
In seismic exploration of the earth, seismic energy is imparted to the earth. This energy travels into the earth and is reflected by the interfaces (reflectors; as used herein, "reflector" means the actual subsurface location of an interface and "reflection" means its apparent location by reference to unmigrated seismic data) between various subsurface formations. In typical seismic exploration, energy is imparted to the earth at a shot point location, and recorded at a number of geophone locations spaced at various distances away from the shot point. These various distances are termed "offsets." The offsets range typically on the order of 50 to 20,000 feet away from the shot point. The shot point is relocated, or a plurality of shot points are used, so as to obtain a plurality of traces at each geophone.
The output signal from each of the geophones is recorded as a function of time. It is desirable to convert this information so that the picture generated by displaying the traces actually corresponds to the depth of the various reflectors within the earth. In order to be able to translate this data into amplitude versus depth, rather than amplitude versus time, information, the velocities of the various subsurface formations must be determined. Accordingly, in order to provide accurate pictures of the subterranean structure of the earth, improved methods of determining the correct velocity of the seismic energy in the subterranean formations are required. These methods generally are performed on computers, particularly supercomputers able to manipulate large amounts of data efficiently.
The term "migration" refers to correction of data which were recorded as a function of time for the velocity of the wave in the subterranean structure. In this process, one can convert a number of offset versus time records, which records can then be displayed to yield a realistic picture of the structure.
Seismic migration requires an accurate model of the subsurface velocity. There are many existing methods for performing migration velocity analysis. Three are of particular significance: iterative prestack migration, prestack migration velocity sweeps and depth focusing analysis. The methods discussed herein all involve iterative prestack migration of the data with different velocities, to obtain an approximation of the velocity by trial and error.
One method for obtaining migration velocities is to prestack migrate subsets (usually common-shot gathers or common offset gathers) of the seismic data with an initial reference migration velocity (Al-Yahya, K. M., "Velocity Analysis by Iterative Profile Migration," Geophysics, 54(6):718-729 (1989); Deregowski, S. M., "Common-Offset Migrations and Velocity Analysis," First Break, 8(6): 224-234 (1990)). If this migration produces images that are consistent for all the data subsets, then the initial guess for the reference velocity is taken to be correct. If this initial migration produces inconsistent images, then these differences can be used to estimate a corrected velocity that is closer to the true velocity than the initial velocity selected. A flow chart for this method is set forth in FIG. 1. It can be seen from this chart that the calculations are entirely sequential, with the result that this method takes not only significant computer time, but also significant interpretation time. This method usually requires several iterations using the updated velocity for prestack migration each time. Unfortunately, this method is very expensive since prestack migration itself is very expensive. In particular, the cost of CPU time in a supercomputer to output a single three-dimensional prestack migrated line is presently on the order of $200,000.
The prestack migration velocity sweep method is closely related to the iterative profile migration method, but performs multiple migrations in parallel rather than sequentially. A migration velocity sweep consists of prestack migrating common-offset gathers simultaneously with several different velocities and summing the migrated images. This produces a set of seismic traces, one group of traces for each velocity, that can be plotted to form a velocity analysis display (see FIG. 2 for flowchart of this method). Velocities that produce consistent images with respect to the different common-offset gathers will produce amplitude peaks on this velocity analysis display. Thus, amplitude peaks on the velocity analysis display can be used to pick the migration velocity function. Because this method involves parallel processing, less interpretation time, but more CPU time, is used than with the iterative prestack migration method.
One problem with this prestack migration velocity sweep velocity analysis method is that amplitude peaks can appear at velocities that do not correspond to consistent imaging of the common-offset gathers. This can lead the interpreter to pick incorrect velocities (Schleicher, K. L., Grygier, D. J., et al., Ed., Migration Velocity Analysis: A Comparison of Two Approaches, 61st Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Tulsa, Soc. Expl. Geophys., 1237-1238 (1991)). These erroneous velocity estimates are the result of dipping reflectors migrating into the velocity analysis location as the migration velocity changes (see FIGS. 3A and 3B). FIGS. 3A and 3B are schematic diagrams illustrating how prestack migration velocity sweeps can produce false velocity picks 6 for dipping reflectors. For the faulted reflector 2 shown therein, notice that the event has not migrated into the velocity analysis location 4 at velocity V.sub.1 (FIG. 3A) but at velocity V.sub.2 (FIG. 3B) the event has migrated into the velocity analysis location. Thus, there will be a relatively high amplitude at velocity V.sub.2, even though velocity V.sub.1 may be the velocity which produces the most consistent image as a function of source-receiver offset.
This prestack migration velocity sweep method is about ten times more computer intensive than iterative prestack migration, because it requires 10 to 50 applications of prestack migration. However, these computer costs may be offset by the reduced interpretation costs, since the velocity interpreter need pick the migration velocity only once.
A third method for velocity analysis is depth focusing analysis. Depth focusing analysis determines velocities by using downward extrapolation to estimate zero-offset seismic traces at a range of depths. These extrapolations to different depths are all performed with one reference migration velocity. If a reflection has an amplitude peak at the depth corresponding to the two-way vertical traveltime through the reference velocity field, then the reference velocity is the correct migration velocity. Deviations from this condition can be used to estimate the error in the reference velocity (Kim, Y. C. and Gonzalez, R., "Migration velocity analysis with the Kirchhoff Integral," Geophysics 56(3): 365-370 (1991); Yilmaz, O. and Chambers, R. E., "Migration Velocity Analysis by Wave-Field Exploration," Geophysics, 49(10):1664-1674 (1984)). This method is usually iterated several times until convergence is achieved.
This method can produce false velocity picks 6 for dipping reflectors, which false picks 6 are similar to those produced by prestack migration velocity sweeps discussed above and shown in FIG. 3. (MacKay, S., and Abma, R., Ed., Depth Focusing Analysis Using a Wavefront-Curvature Criterion, 62nd Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Tulsa, Soc. Expl. Geophys, 927 (1992)). Furthermore, this method may not converge for steeply dipping reflectors (MacKay, S. and Abma, R., "Imaging and Velocity Estimation with Depth-Focusing Analysis," Geophysics, 57(12): 1608-1622 1992).
All the velocity analysis methods discussed above require several applications of prestack migration. Therefore, reducing the cost of prestack migration would have a significant positive impact on the cost of any of these velocity analysis methods.
One way of reducing the cost of prestack migration is to use an inherently fast technique for migration. There are three commonly used wave-equation migration algorithms: frequency-wavenumber migration, finite-difference migration, and Kirchhoff migration. Frequency wavenumber migration and finite-difference migration are generally faster than Kirchhoff migration; however, Kirchhoff migration has several advantages that have made it the method of choice for three-dimensional prestack migration.
First, Kirchhoff migration can handle irregular shooting geometries, such as those commonly encountered in unstacked three-dimensional data. Second, complex migration velocity fields can be used with Kirchhoff migration. Third, Kirchhoff methods can migrate reflectors having very steep dip. Finally, Kirchhoff migration can be used in a target-oriented mode. In this mode, images at a few selected target locations can be produced at a fraction of the cost of using Kirchhoff migration to produce images at all possible output locations. Frequency-wavenumber migration fails with irregular shooting geometries or complex migration fields, while finite-difference migration fails with irregular shooting geometries or reflectors with a very steep dip. Neither frequency-wavenumber nor finite difference migration can be used in a target-oriented mode. These methods must compute the migrated image at all possible output locations. This is important for migration velocity analysis, because velocity analysis can usually be performed at a small fraction of the number of locations at which a seismic image is desired. Therefore, using target-oriented Kirchhoff migration for velocity analysis can be cost competitive with the inherently faster frequency-wavenumber and finite-difference methods. Because of the limitations of these methods, only methods for speeding up Kirchhoff migration were explored for the method of this invention.
The migration techniques proposed herein could be used with non-Kirchhoff migration methods. However, the techniques proposed here achieve their greatest gain in efficiency when used with migration methods that can operate in a target-oriented mode. Therefore, the frequency-wavenumber and finite difference methods would not achieve efficiency gains as great as would the Kirchhoff method, because they cannot operate in a target-oriented mode. However, there may be other migration methods, such as Gaussian beam migration (Hill, N. R., "Gaussian Beam Migration," Geophysics 55(11):1416-1428), that would benefit from incorporating limited aperture migration.
The equations describing Kirchhoff migration are well known in the art (Berryhill, J. R., Ed. Wave Equation Datuming Before Stack, 54th Annual International Mtg. Soc. Expl. Geophys., Expanded Abstracts, Tulsa, Soc. Expl. Geophys., Session:S2.6 (1984); Schneider, W. A., "Integral Formulation for Migration in Two-Dimensions and Three-Dimensions," Geophysics 43(1): 49-76 (1978)). Kirchhoff migration involves summing the input seismic traces along traveltimes corresponding to a point diffractor in the subsurface (see FIG. 4). The migration aperture is defined as all the traces included in this summation for a given output trace. The aperture is usually limited to those traces which have both source and receiver within a specified distance from the output trace location (usually about 5,000 to 25,000 feet).
FIG. 4 is a schematic diagram illustrating the Kirchhoff migration method. Input traces are summed along the Kirchhoff summation curve 8 (diffraction traveltime curve) and output at the apex of the curve 12. The aperture 14 contains all traces within a specified distance of the output location. For the reflection 10 shown in FIG. 4, only those traces within the shaded area 16 contribute significantly to the sum.
Those input traces which contribute significantly have diffraction raypaths that are close to an actual reflection raypath (see FIG. 5). FIG. 5 is an illustration of which input traces will make significant contribution to the migrated image of a reflector 17. Sources are indicated by 19 and receivers are indicated by 21. Notice that the traces that contribute significantly 22 will have diffraction raypaths to the imaging point that are close to a reflection raypath 20 for that point, while those traces 18 which do not contribute significantly have diffraction raypaths to the imaging point that are not close to a reflection raypath 20 for that point. Thus, given knowledge of the reflection raypaths 20, raytracing can be used to determine which traces 22 will contribute significantly to the output migrated trace. Raytracing is a technique familiar to those of reasonable skill in the art. Including only those traces that contribute significantly in the Kirchhoff summation speeds up two-dimensional prestack migration by about a factor of 10 and speeds up three-dimensional prestack migration by about a factor of 100.
Just such a method has been developed by Carroll et. al. (Carroll, R. J., Hubbard, L. M., et al., "A Directed-Aperture Kirchhoff Migration," Geophysical Imaging, Symposium of Geophysical Society of Tulsa, Tulsa, Soc. Expl. Geophys., 151-165 (1987)). They have developed a method for reducing the cost of Kirchhoff prestack migration. They first make a reflector model, based on stacked seismic data. Raytracing is used to determine the locations of sources and receivers that will contribute significantly to the prestack migration of each reflector. They then define a time-varying aperture for prestack migration, centered on these raytraced locations, that is, significantly narrower than a conventional migration aperture (see FIG. 6). FIG. 6 is a schematic diagram illustrating Carroll et. al.'s directed-aperture migration method. Migration hyperbolas are indicated by 28. Normal incidence ray tracing is used to determine the directed aperture 26 used to produce a migrated trace at the output location 30. Since computer CPU time for Kirchhoff migration is proportional to the aperture size, this reduction in aperture should greatly reduce the cost of prestack migration. Carroll et al. call this method directed-aperture migration, since the location of the aperture is moved to different locations depending on a model of the reflectors 24.
The method of Carroll et. al. should significantly reduce the CPU time for prestack migration; however, their method presents a problem. The method still requires reading a large fraction of the input traces to produce a migrated output trace at one location. The reason for this is that the Carroll et al. aperture varies with time; different sets of input traces contribute to the output trace at different times (see FIG. 6). Thus, even though only a small percentage of the input traces contribute at any particular time on the output trace, a much larger percentage of the input traces are required to form all the time samples of an output trace. This problem intuitively means that computer I/O costs will probably not be significantly reduced, even though the CPU costs should be reduced.
It is an object of this invention to present a method for performing prestack migration at a dramatically reduced cost.
It is a further object of this invention to present a method for calculating subsurface velocities at a dramatically reduced cost.
It is a further object of this invention to present a method for calculating subsurface velocities more quickly and more accurately than is possible using current methods.
It is a further object of this invention to eliminate false velocity picks in the determination of subsurface velocities.
It is a further object of this invention to present a method for building an accurate three-dimensional migration velocity from a grid of two-dimensional lines.
It is a further object of this invention to present a method for accurately migrating an existing three-dimensional stack without incurring the large expense of obtaining and reprocessing the three-dimensional unstacked tapes.
It is a further object of this invention to significantly improve the signal-to-noise ratio (S/N) of velocity analysis displays.
Further objects and advantages of this invention will be seen by one skilled in the art of geophysical data processing upon review of the specification, figures and claims herein.